Joint seminar co-organized by the Depart of Algebra and Number Theory and the International Center for Research and Postgraduate Training in Mathematics (ICRTM-VAST)

Speaker: Trung Chau (Chennai Mathematical Institute, India)

Venue: Room 612, Building A6

Time: 9h30-11h, June 24th

Abstract: Homological shift ideals were introduced by Herzog, Moradi, Rahimbeigi, and Zhu in 2020. Given a monomial ideal $I$, the $k$-th homological shift ideal of $I$ is defined to be the monomial ideal generated by the multigraded shifts of the minimal free resolution of $I$, and denoted by $HS_k(I)$. In particular, $HS_0(I)=I$. We say that $I$ has homological linear quotients if all of its homological shift ideals have linear quotients. In this talk, I will discuss the property of having homological linear quotients for edge ideals of graphs, together with the rigidity of homological shift ideals having linear quotients. This is joint work with Kanoy Kumar Das and Aryaman Maithani.